practice
choose the correct answer.
1. a model of the equation 4n + 2 = 10 is shown.
image of model: 4 rectangles labeled n, 2 rectangles labeled 1, equal to 10 small squares labeled 1
what value of n makes the equation true?
a. n = 2
b. n = 3
c. n = 4
d. n = 8
2. what value of z makes this equation true?
$\frac{z}{4} = 12$
a. z = 3
b. z = 8
c. z = 16
d. z = 48
3. what value of x makes 6x − 3 = 39 true?
a. x = 6
b. x = 7
c. x = 30
d. x = 252
4. one van can seat 8 people. how many vans would be needed to transport a total of 36 people?
a. 3
b. 4
c. 5
d. 6
5. angelo has 4 fewer than twice as many video games as lucia has. angelo has 24 video games. how many video games does lucia have?
a. 6
b. 10
c. 12
d. 14
6. grady bought 7 books, each the same price. after using a $10-off coupon, the total charge was $28.50. what was the cost of each book?
a. $2.64
b. $4.07
c. $5.50
d. $38.50

Question

Accepted Answer

### Question 1
# Explanation:
## Step1: Analyze the equation $4n + 2 = 10$
Subtract 2 from both sides: $4n=10 - 2=8$
## Step2: Solve for $n$
Divide both sides by 4: $n=\frac{8}{4}=2$
# Answer: A. $n = 2$

### Question 2
# Explanation:
## Step1: Analyze the equation $\frac{z}{4}=12$
Multiply both sides by 4: $z = 12\times4$
## Step2: Calculate $z$
$z=48$
# Answer: D. $z = 48$

### Question 3
# Explanation:
## Step1: Analyze the equation $6x-3 = 39$
Add 3 to both sides: $6x=39 + 3=42$
## Step2: Solve for $x$
Divide both sides by 6: $x=\frac{42}{6}=7$
# Answer: B. $x = 7$

### Question 4
# Explanation:
## Step1: Set up the division
Number of vans $=\frac{36}{8}=4.5$
Since we can't have half a van, we round up to the next whole number.
## Step2: Determine the number of vans
4 vans would seat $4\times8 = 32$ people (not enough), 5 vans would seat $5\times8=40$ people (enough). But wait, wait, let's recalculate: $36\div8 = 4.5$, so we need 5 vans? Wait no, wait the options: A.3, B.4, C.5, D.6. Wait $4\times8 = 32$, $5\times8 = 40$. Since 36 is more than 32, we need 5? Wait no, maybe I made a mistake. Wait $36\div8 = 4.5$, so we need to round up to 5? But let's check the options. Wait the options are A.3, B.4, C.5, D.6. Wait $4\times8 = 32$, $5\times8 = 40$. So 4 vans can seat 32, which is less than 36, so we need 5. So the answer is C? Wait no, wait maybe the problem is that maybe it's a trick? Wait no, $36\div8 = 4.5$, so we need 5 vans. So answer is C.
Wait, let's do it again: Number of vans $=\lceil\frac{36}{8}
ceil=\lceil4.5
ceil = 5$
# Explanation:
## Step1: Calculate $36\div8$
$36\div8 = 4.5$
## Step2: Round up to the nearest whole number
Since we can't have a fraction of a van, we need 5 vans.
# Answer: C. 5

### Question 5
# Explanation:
## Step1: Let Lucia's video games be $x$
Angelo's video games: $2x-4 = 24$
## Step2: Solve for $x$
Add 4 to both sides: $2x=24 + 4=28$
Divide by 2: $x=\frac{28}{2}=14$? Wait no, wait the options: A.6, B.10, C.12, D.14. Wait $2x-4 = 24$, so $2x=28$, $x = 14$? But the options have D.14? Wait no, wait the question says "Angelo has 4 fewer than twice as many as Lucia". So $A = 2L-4$, $24=2L - 4$, so $2L=28$, $L = 14$. So answer is D? Wait the options are A.6, B.10, C.12, D.14. So D.
Wait, let's do it step by step:
## Step1: Define variable
Let $L$ be Lucia's video games.
## Step2: Set up equation
$2L-4 = 24$
## Step3: Solve for $L$
Add 4: $2L=28$
Divide by 2: $L = 14$
# Answer: D. 14

### Question 6
# Explanation:
## Step1: Let the cost of each book be $x$
Total cost before coupon: $7x$
After coupon: $7x-10 = 28.50$
## Step2: Solve for $x$
Add 10 to both sides: $7x=28.50 + 10=38.50$
Divide by 7: $x=\frac{38.50}{7}=5.50$
# Answer: C. \$5.50

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Analyze the equation \(4n + 2 = 10\)

Step2: Solve for \(n\)

Step1: Analyze the equation \(\frac{z}{4}=12\)

Step2: Calculate \(z\)

Step1: Analyze the equation \(6x-3 = 39\)

Step2: Solve for \(x\)

Answer:

Question 2